A lower bound on the growth exponent for loop-erased random walk in two dimensions

 Access to full text

 Full (PDF)

1. [1] Ahlfors L., Conformal Invariance. Topics in Geometric Function Theory. McGraw-Hill ( 1973). Zbl0272.30012MR357743
2. [2] Billingsley P., Probability and Measure. 2nd ed., John Wiley ( 1986). Zbl0649.60001MR830424
3. [3] Burdzy K. and Lawler G., Rigorous exponent inequalities for random walks. J. Phys. A. 2 3 ( 1990) L23-L28. Zbl0716.60080MR1034620
4. [4] Duplantier B., Loop-erased self-avoiding walks in 2D. Physica A 191 ( 1992) 516-522. 
5. [5] Fargason C., The percolation dimension of Brownian motion in three dimensions. Ph.D. dissertation, Duke University ( 1998). Zbl0907.60069
6. [6] Guttmann A. and Bursill R., Critical exponent for the loop-erased self-avoiding walk by Monte Carlo methods. J. Stat. Phys. 59 ( 1990) 1-9. 
7. [7] Kenyon R., The asymptotic distribution of the discrete Laplacian ( 1998) preprint. 
8. [8] Kesten H., Hitting probabilities of random walks on ℤd. Stoc. Proc. Appl. 25 ( 1987) 165-184. Zbl0626.60067MR915132
9. [9] Lawler G., Intersections of Random Walks. Birkhäuser-Boston ( 1991). Zbl0925.60078MR1117680
10. [10] Lawler G., A discrete analogue of a theorem of Makarov. Comb. Prob. Computing 2 ( 1993) 181-199. Zbl0799.60062MR1249129
11. [11] Lawler G., The logarithmic correction for loop-erased walk in four dimensions, Proceedings of the Conference in Honor of Jean-Pierre Kahane (Orsay 1993), special issue of J. Fourier Anal. Appl. ( 1995) 347-362. Zbl0889.60075MR1364896
12. [12] Lawler G., Cut points for simple random walk. Electron. J. Prob. 1 ( 1996) 13. Zbl0888.60059MR1423466
13. [13] Lawler G., Loop-erased random walk, preprint, to appear in volume in honor of Harry Kesten ( 1998). Zbl0947.60055MR1703133
14. [14] Lawler G. and Puckette E., The intersection exponent for simple random walk ( 1998) preprint. Zbl0974.60088MR1810151
15. [15] Madras N. and Slade G., The Self-Avoiding Walk. Birkhäuser-Boston ( 1993). Zbl0780.60103MR1197356
16. [16] Majumdar S.N., Exact fractal dimension of the loop-erased self-avoiding random walk in two dimensions, Phys. Rev. Lett. 68 ( 1992) 2329-2331. 
17. [17] Pemantle R., Choosing a spanning tree for the integer lattice uniformly. Ann. Prob. 19 ( 1991) 1559-1574. Zbl0758.60010MR1127715
18. [18] Propp J. and Wilson D., How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph. J. Algorithms (to appear). Zbl0919.68092MR1622393
19. [19] Pommerenke C., Boundary Behaviour of Conformal Maps, Springer-Verlag ( 1992). Zbl0762.30001MR1217706
20. [20] Werner W., Beurling's projection theorem via one-dimensional Brownian motion. Math. Proc. Cambridge Phil. Soc. 119 ( 1996) 729-738. Zbl0854.60083MR1362952

1. Daisuke Shiraishi, Heat kernel for random walk trace on ℤ3 and ℤ4